Not with my bank. With my Chase BA Visa, I have a single password that I have successfully used for several years with the "Verified by Visa" program. It is not a numeric code, simply a password that I was asked to choose for myself. Perhaps different banks use the program differently, but the "Verified by Visa" website describes the process with a permanent password, not a transaction-specific code:

"If your issuer is participating in Verified by Visa you may be asked to complete a brief activation process. To complete the process, you will verify your identity by answering a few simple questions then create your Verified by Visa password and you are done. Once your card is activated, your card number will be recognized whenever you shop at a participating Verified by Visa merchant. You will enter your password in the Verified by Visa window, your identity will be verified and the transaction will be completed."

Here is the VbV web site: https://usa.visa.com/personal/security/vbv/index.jsp